Two-dimensional NACA0012 Airfoil Research Articles

Hybrid method for wall local refinement in lattice Boltzmann method simulation

The recent development of the lattice Boltzmann method enables its widespread application in various industrial areas. However, in the simulation of complicated industrial problems, considerable grid numbers are required to achieve reasonable resolution in the near-wall region due to the lack of a local refinement method on the geometry. This study proposes a new hybrid grid refinement method, which comprises the reconstruction algorithm in refined near-wall nodes on the refinement interface and the in-domain interpolation multi-grid method to prevent the local distortion of the pseudo-wall among resolution levels. The proposed method is validated on a two-dimensional flat plate and NACA0012 airfoil at low and high Reynolds numbers. Furthermore, the aerodynamic and aeroacoustics of a pair of counter-rotating propellers are simulated with the proposed lattice Boltzmann method and compared with the results obtained using commercial software.

Two-dimensional simulation of frost formation on the NACA0012 airfoil under strong convection by using the p-VOF method

A newly developed frosting simulation method, p-VOF method, is applied to simulate the dynamic frost formation on the NACA0012 airfoil under strong convection. The p-VOF method is a pseudo VOF method of the multiphase flow simulation with phase change. By solving a simplified mass conservation equation explicitly instead of the original volume fraction equations in CFD software, the efficiency and robustness of calculation are greatly improved. This progress makes it possible to predict a long-time frost formation. The p-VOF method was successfully applied to the simulation of dynamic frosting on the two-dimensional NACA0012 airfoil under strong convection conditions with constant frost physical properties. The simulation result shows that the average thickness of the frost layer increases, and the frost bulges and flow separation appear earlier, when the airfoil surface temperature decreases or the air humidity increases. The frost bulges and flow separation appear earlier, when the air velocity is faster, the growth rate of the frost layer at the early stage is greater, but the final frost layer is thinner.

Study on dynamics of vortices in dynamic stall of a pitching airfoil using Lagrangian coherent structures

The evolution of vortex structure and mass transport process during dynamic stall of the two-dimensional pitching NACA0012 airfoil are studied in detail, using Lagrangian coherent structures (LCSs), and the nature of dynamic stall is given from viewpoint of nonlinear dynamics. First, the numerical method with SST k−ω turbulence model is used to simulate the flow field around the pitching oscillation airfoil. Then, the Lagrangian-averaged vorticity deviation (LAVD) method is used to analyze the formation and evolution of vortex structure during dynamic stall. Further, the circulation development process of the primary leading edge vortex (LEV) is studied, with comparison between LAVD method with Q criterion. Finally, the dynamic behaviors, such as the mass transport and evolution of flow structure during the process of dynamic stall, are analyzed in depth by using LCSs, and the fluctuation of lift coefficient and the dynamic stall are investigated from the viewpoint of nonlinear dynamics. The results show that the evolution of vortex structure and mass transport are closely related to the fluctuation of lift coefficient during the dynamic stall, and the low-pressure region formed by vortices and the complex mass transport and mixing process on the suction surface of the airfoil are the main reasons for the high lift during the dynamic stall process. In particular, the primary LEV, which can be accurately identified and tracked by LAVD method, plays a very important role in lift enhancement, and the primary LEV and the secondary LEV form and grow in turn by the intermittent feeding process of shear layer. Additionally, the fluid particles in front of the leading edge of the airfoil enter the LEV through a special mass transport channel, which is textured by LCSs and opened and closed intermittently. More importantly, the saddle point of LCSs is an important component of vortex boundary, and its dynamic behaviors represent the behaviors of vortex. The first separation of saddle point from the shear layer at leading edge indicate the separation of primary LEV from the suction surface of the airfoil, and the occurrence of dynamic stall. The second separation of saddle point from the shear layer at leading edge indicate that primary LEV begins to leave the upper region of the airfoil, corresponding to a sharp drop in lift coefficient. Generally, compared to the traditional visualization techniques, the Lagrangian analysis based on LCSs and LAVD can provide a deeper insight into the dynamics of the vortex in flow field around pitching oscillation airfoil and the dynamic mechanism of dynamic stall.

Aeroacoustic noise calculations of non-compact bodies with permeable boundaries

A hybrid computational aeroacoustic method with permeable boundary is developed to evaluate non-compact noise induced by low Mach number flow over arbitrarily shaped bodies. Based on Lighthill’s equation and the boundary element method, the unified integral equations are established in which the integral boundary surrounding the objects can be selected arbitrarily. Validation studies are developed for noise induced by two-dimensional NACA0012 airfoil and three-dimensional circular cylinder. For NACA0012 airfoil, the directivity patterns of calculated noise with different permeable boundaries agree well with Howe’s analytical solution for trailing edge model. The acoustic noise generated by circular cylinder has a good agreement with Revell’s experimental data and FW-H equation. It demonstrates that the noise predicted by different permeable boundary is as accurate as that calculated by the body surface.

Aerodynamic Optimization of Wing by Camber Morphing using Cfd

This paper presents the CFD analysis of the 2-Dimensional NACA0012 airfoil carried out for identifying its aerodynamic coefficients (Lift and Drag coefficients), then further implementing morphing technology on the same two-dimensional NACA0012 airfoil, again carrying out CFD analysis to determine its aerodynamic coefficients (Lift coefficient (CL) and Drag coefficient (CD), then comparing the results of both the airfoil shapes particularly to the amount of Lift generated to prove that morphing airfoil produces more amount of Lift when compared to typical airfoil shapes. Using ANSYS Design modeler airfoil geometry was created and morphing shape could be achieved by XFLR5 software further the analysis is carried out using FLUENT 18.1 at subsonic flow. This morphing enables to improve aerodynamic efficiency.

Unsteady Preconditioned Characteristic Boundary Conditions for Direct Numerical Simulation of Incompressible Flows

The unsteady preconditioned characteristic boundary conditions (UPCBCs) based on the artificial compressibility (AC) method are formulated and applied at artificial boundaries for the direct numerical simulation (DNS) of incompressible flows. The compatibility equations including the unsteady terms are mathematically derived in the generalized curvilinear coordinates and then incorporated as boundary conditions (BCs) in a high-order accurate incompressible flow solver. The spatial derivative terms of the system of equations are discretized using the fourth-order compact finite difference (FD) scheme, consistent with the high-order accuracy required for the DNS. The time integration is carried out using an implicit dual time-stepping method, and the robustness and performance of the numerical algorithm are enhanced by applying the preconditioning technique and calculating the automated AC parameter based on the local flow conditions. At first, the steady viscous incompressible flow for a two-dimensional plane jet is computed to assess the accuracy and performance of the solution method by applying the UPCBCs in comparison with the simplified BCs. Then, the simulation of the unsteady incompressible viscous flow around a two-dimensional NACA0012 airfoil at the Reynolds number 800 and the angle of attack 20° is performed, and it is indicated that the computational cost of the solution is considerably decreased by implementing the UPCBCs at the artificial far-field boundary compared with the simplified BCs, which is remarkably valuable for the DNSs. Finally, the computation of the transition to unsteady for the incompressible flow around a three-dimensional NACA0012 wing at the same conditions of the two-dimensional case is successfully performed, and the results obtained are compared with those of previous studies that exhibit good agreement. Indications are that the present solution method by applying the UPCBCs at the artificial far-field boundary can be effectively used for the DNSs of the incompressible flows.

Accurate Computation of Airfoil Flow Based on the Lattice Boltzmann Method

The lattice Boltzmann method (LBM) is an important numerical algorithm for computational fluid dynamics. This study designs a two-layer parallel model for the Sunway TaihuLight supercomputer SW26010 many-core processor, which implements LBM algorithms and performs optimization. Numerical experiments with different problem sizes proved that the proposed model has better parallel performance and scalability than before. In this study, we performed numerical simulations of the flows around the two-dimensional (2D) NACA0012 airfoil, and the results of a series of flows around the different angles of attack were obtained. The results of the pressure coefficient and lift coefficient were in good agreement with those in the literature.

Dynamic mesh method based on diffusion equation and nodal rotation for high-aspect-ratio composite wings

In this paper a dynamic mesh method based on diffusion equation and nodal rotation is developed for high-aspect-ratio composite wings. Mesh displacement is described by diffusion equation and calculated by finite element method. The mesh was distorted because the displacement of the mesh nodes is uncoupled in different directions, and its quality diminished due to large deformation. The nodal rotational method is introduced to solve this problem. The technique used the same diffusion equation to describe the rotational angle and is solved by the finite element method. The node nearest the wall boundary is the rotational centre and the corresponding rotational vector is the rotational axis. The new position of the mesh node is obtained by rotating transformation. The mesh deformation of two-dimensional NACA0012 airfoil mesh, three-dimensional spherical mesh and high aspect ratio composite wings are verified for various cases. The results show that the present method is applicable to structural and unstructured/hybrid meshes. The mesh quality is improved and its overlap and negative volume are effectively prevented under large deformation.

Simulation and Modeling of Rigid Aircraft Aerodynamic Responses to Arbitrary Gust Distributions

The stresses resulting from wind gusts can exceed the limit value and may cause large-scale structural deformation or even failure. All certified airplanes should therefore withstand the increased loads from gusts of considerable intensity. A large factor of safety will make the structure heavy and less economical. Thus, the need for accurate prediction of aerodynamic gust responses is motivated by both safety and economic concerns. This article presents the efforts to simulate and model air vehicle aerodynamic responses to various gust profiles. The computational methods developed and the research outcome will play an important role in the airplane’s structural design and certification. Cobalt is used as the flow solver to simulate aerodynamic responses to wind gusts. The code has a user-defined boundary condition capability that was tested for the first time in the present study to model any gust profile (intensity, direction, and duration) on any arbitrary configuration. Gust profiles considered include sharp edge, one minus cosine, a ramp, and a 1-cosine using tabulated data consisting of gust intensity values at discrete time instants. Test cases considered are a flat plate, a two-dimensional NACA0012 airfoil, and the high Reynolds number aero-structural dynamics (HIRENASD) configuration, which resembles a typical large passenger transport aircraft. Test cases are assumed to be rigid, and only longitudinal gust profiles are considered, though the developed codes can model any gust angle. Time-accurate simulation results show the aerodynamic responses to different gust profiles including transient solutions. Simulation results show that sharp edge responses of the flat plate agree well with the Küssner approximate function, but trends of other test cases do not match because of the thin airfoil assumptions made to derive the analytical function. Reduced order aerodynamic models are then created from the convolution integral of gust amplitude and the time-accurate responses to sharp-edge gusts. Convolution models are next used to predict aerodynamic responses to arbitrary gust profiles without the need of running time-accurate simulations for every gust shape. The results show very good agreement between developed models and simulation data.

Steady Aerodynamic Characteristics of Two-Dimensional NACA0012 Airfoil for One Revolution Angle of Attack

Steady variations in aerodynamic forces and flow behaviors of two-dimensional NACA0012 airfoil were investigated using a numerical method for One Revolution Angle of Attack (AOA) at Reynolds number of $$10^{5}$$ . The profiles of lift coefficients, drag coefficients, and pressure coefficients were compared with those of the experimental data. The AERODAS model was used to analyze the profiles of lift and drag coefficients. Wake characteristics were given along with the deficit profiles of incoming velocity components. Both the characteristics of normal and reverse airfoil models were compared with the basic aerodynamic data for the same range of AOA. The results show that two peaks of the lift coefficients appeared at $$11.5{^{\circ }}$$ and $$42{^{\circ }}$$ and are in good agreement with the pre-stall and post-stall models, respectively. Counter-rotating vortex flows originated from the leading and trailing edges at a high AOA, which formed an impermeable zone over the suction surface and made reattachments in the wake. Moreover, the acceleration of inflow along the boundary of the vortex wrap appeared in the profile of the wake velocity. The drag profile was found to be independent of the airfoil mode, but the lift profile was quite sensitive to the airfoil mode.

Implementation and comparison of three isogeometric Navier–Stokes solvers applied to simulation of flow past a fixed 2D NACA0012 airfoil at high Reynolds number

Implementation of three different Navier–Stokes solvers in an isogeometric finite element framework is presented in this paper. The three solvers Chorin projection method and Coupled formulation, both with the Spalart–Allmaras turbulence model, and Variational Multiscale (VMS) method have been applied to simulate flow past a two-dimensional NACA0012 airfoil at a high Reynolds number (Re=3×106) for four different angles of attack. The predicted flow characteristics have been compared and the effects of increasing the order of the spline element on the accuracy of prediction and computational efficiency are evaluated. In this study it turns out that flow separation does not take place up to an angle of attack of 16°. Up to this angle of attack all three solvers predict similar results in good agreement with each other and with available experimental results. However, a big spread in lift and drag coefficients is observed in the stall regime. Our study also shows that for linear spline elements all three solvers are computationally similar. For quadratic spline elements the Chorin solver compares favorably to the others based on the results presented here.

Improved methodologies for the design of maneuver for stability and control simulations

With many modern fighter aircraft experiencing unpredicted flight dynamics during flight tests, recent research has focused on developing methodologies for incorporating computational fluid dynamics into the aircraft development process. The goal of this approach is to identify configurations susceptible to stability and control issues early in the design process. Previous research has primarily focused on full aircraft configurations, however, to increase the rate of development the current study focused on a two-dimensional NACA0012 airfoil. The two-dimensional NACA0012 airfoil has the advantage of reducing the computational cost by orders of magnitude compared to full scale aircraft simulations, while still providing complicated aerodynamics at high angles of attack. Computationally predicted lift coefficients from a number of newly developed training maneuvers were used to generate reduced order aerodynamic loads models. For evaluation, these models were compared to generated static and dynamic validation data. Methods of improving both the computational training maneuver and the reduced order modeling approach are suggested.

High-order numerical simulations of the flow around a heaving airfoil

We simulate the incompressible, viscous flow over a two-dimensional NACA0012 airfoil oscillating in heave at mean incidences 12 ° < α ¯ < 20 ° and Reynolds numbers 800 ⩽ Re ⩽ 10 4. The two-dimensional Navier–Stokes equations are solved using a Spectral/ hp Element Method for the spatial discretization and a high-order splitting scheme for the evolution in time. A moving-frame of reference technique accounts for the airfoil motion. We consider the effects on the aerodynamical flow and the force coefficients caused by the variation of the mean incidence, the Reynolds number and the sinusoidal heave motion of the airfoil. The numerical simulations are in good agreement with previously published experimental and computational work, in particular the increase in the force coefficients due to the increase in the Reynolds number and/or the mean incidence are confirmed by the present study. Furthermore, we present here new details of the spatio-temporal non-linear flow pattern evolution where for the first time the Spectral/ hp Element Method associated with the moving frame of reference is used for this kind of flow.

Numerical Study of Flexible Flapping Wing Propulsion

In this study, a strong-coupling approach is applied to simulate highly flexible flapping wings interacting with fluid flows. Here, the fluid motion, solid motion, and their interaction are solved together by a single set of equations of motion on a fixed Eulerian mesh, with the elastic stress being solved on a Lagrangian mesh and projected back to the Eulerian mesh. To provide necessary flapping mechanism, control cells are implemented in solid area (i.e., the wing) as skeleton. The moving trajectory of the skeleton is therefore prescribed by a conventional direct-forcing type of immersed boundary method, while the rest of the wing moves passively through elasticity and fluid-structure interaction. This combined algorithm is then used to study the propulsion characteristics of flexible flapping wings with different elastic moduli and at different flapping frequencies and amplitudes. A two-dimensional NACA0012 airfoil is chosen as a model wing, and it is under active plunging defined by control cells and corresponding passive pitching motion. With different input parameters, very different wake structures can be observed. As a result, the coupled plunging-pitching motion can be either drag-producing or thrust-producing. Finally, passive pitching angle θ and nominal angle of attack α for flexible wings are defined to characterize the flapping motion. It is found that θ needs to be greater than 0.26 and α needs to be greater than 0.3 to generate thrust instead of drag for the flapping motion within the current parametric matrix.

Numerical Study of Heat Transfer Around the Small Scale Airfoil Using Various Turbulence Models

A numerical investigation of low-Reynolds number flows with thermal effect around the MAV airfoils using various turbulence models, including an algebraic Baldwin-Lomax model, Spalart-Allmaras one equation, and two equation (k-ω and SST-k-ω) turbulence models, is presented. First, the thermal effect on the aerodynamic efficiency is studied for flow around a rectangular MAV wing, based on the NACA0012 airfoil section at low-aspect ratio (AR = 2) and an angle of attack equal to 0°. Second, details of the thermal effect are limited to the two-dimensional NACA0012 airfoil with chord length of 3.81 cm. This study shows that the improvement of aerodynamic efficiency (increase lift and reduce drag) is achieved by the generation of a temperature difference between extrados and intrados of the airfoil (by cooling the upper surface and heating the lower surface). The numerical results obtained with various turbulence models are in good agreement with experiment data, except the k-ω turbulence model. These results are performed with the CFD-FASTRAN code, using the fully implicit scheme for time integration and the upwind Roe flux difference splitting scheme for space discretization augmented by a high order Osher-Chakravarthy limiter.

Numerical investigation on a transition prediction model

A new transition prediction model is introduced, which couples the intermittency effect into the turbulence transport equations and takes the characteristics of fluid transition into consideration to mimic the exact process of transition. Test cases include a two-dimensional incompressible plate and a two-dimensional NACA0012 airfoil. Performance of this transition model for incompressible flows is studied, with numerical results consistent to experimental data. The requirement of grid resolution for this transition model is also studied.

Surface pressure and aerodynamic loads determination of a transonic airfoil based on particle image velocimetry

The present investigation assesses a procedure to extract the aerodynamic loads and pressure distribution on an airfoil in the transonic flow regime from particle image velocimetry (PIV) measurements. The wind tunnel model is a two-dimensional NACA-0012 airfoil, and the PIV velocity data are used to evaluate pressure fields, whereas lift and drag coefficients are inferred from the evaluation of momentum contour and wake integrals. The PIV-based results are compared to those derived from conventional loads determination procedures involving surface pressure transducers and a wake rake. The method applied in this investigation is an extension to the compressible flow regime of that considered by van Oudheusden et al (2006 Non-intrusive load characterization of an airfoil using PIV Exp. Fluids 40 988–92) at low speed conditions. The application of a high-speed imaging system allows the acquisition in relatively short time of a sufficient ensemble size to compute converged velocity statistics, further translated in turbulent fluctuations included in the pressure and loads calculation, notwithstanding their verified negligible influence in the computation. Measurements are performed at varying spatial resolution to optimize the loads determination in the wake region and around the airfoil, further allowing us to assess the influence of spatial resolution in the proposed procedure. Specific interest is given to the comparisons between the PIV-based method and the conventional procedures for determining the pressure coefficient on the surface, the drag and lift coefficients at different angles of attack. Results are presented for the experiments at a free-stream Mach number M = 0.6, with the angle of attack ranging from 0° to 8°.

Numerical investigation of the tone noise mechanism over laminar airfoils

This paper presents the first numerical investigation via direct numerical simulation of the tone noise phenomenon occurring in the flow past laminar airfoils. This phenomenon corresponds to the radiation of discrete acoustic tones in some specific flow conditions, and has received much attention since the 1970s, and several experimental studies have been carried out to identify and understand the underlying physical mechanisms. However, several points remain to be clarified in order to provide a complete explanation of its origin. The flow around a two-dimensional NACA0012 airfoil is considered in order to have a deeper understanding of the tone noise phenomenon. Consistently with previous experimental studies, it is shown that depending on the Reynolds number and angle of attack, two different types of acoustic spectrum are observed: one which exhibits a broadband contribution with a dominant frequency together with a sequence of regularly spaced discrete frequencies, while the other one is only characterized by a simple broadband contribution. The first configuration is typical of the tone noise phenomenon. The present work shows that in this case, the mean flow on the pressure side of the airfoil exhibits a separation bubble near the trailing edge and the main tone frequency is close to the most amplified frequency of the boundary layer. The mechanism proposed in previous works for the main tone generation – which implies the existence of a separation bubble at the pressure side – is therefore validated by numerical simulation. On the other hand, the analysis of the suction side boundary layer reveals that there is no separation and that the most amplified frequency is different from the main tonal one. However, the suction side boundary layer is highly receptive to the tone frequency. Finally, an original explanation for the existence of the secondary discrete frequencies observed in the radiated pressure spectrum is given. They are associated to a bifurcation of the airfoil wake from a symmetric to a non-symmetric vortex pattern. A possible explanation for the existence of this bifurcation is the interaction between the disturbances which are the most amplified by the suction side boundary layer and those originating in the forcing of the suction side flow by the main tone noise mechanism.

Analysis of Aerodynamic Sound Sources in a Flow Around a Two-Dimensional Airfoil Under Stalled Conditions

In this paper, we discuss an identification of aerodynamic sound sources in a flow around a two-dimensional NACA0012 airfoil at a Reynolds number of 2×105 to 5×105 under stalled conditions. This study is carried out mainly by experimental method based on the results by the measurement of surface pressure, unsteady flow, resulting far-field sound with high accuracy. Also, the computation was performed by Large-Eddy Simulation (LES) for an incompressible flow. Then, we investigated under the light stall condition (LS) when long bubble formed and under the deep stall condition (DS) when completely stalled. As a result, peaks were observed at a Strouhal number of 0.5 to 0.6 not only in aerodynamic sound spectra but also in surface pressure spectra, the coherence spectra between surface pressure and aerodynamic sound, and the coherence spectra between flow velocity and aerodynamic sound. The flow measurements indicate that the vortices based on Strouhal number of 0.5 to 0.6 formed outside of the separated shear layer. Also, some results showed that strong sound sources existed near the airfoil surface in LS but the sound sources disappeared in DS. This is due to the difference in whether the separated flow passes near the suction surface or not.

OS9-10 翼周りの流れと騒音の受動的制御による揚力・抗力への影響(OS9 熱流動,循環型社会における動力エネルギー技術)

In this paper we attempted to reduce the aerodynamic noise generated from a two-dimensional NACA0012 airfoil at a Reynolds number of 3×10^5 in post-stall condition by passive flow and noise control on airfoil surface with various materials. The experimental results showed that the Pile Fabrics reduced the aerodynamic noise with 4.4dB in post-stall condition, but in spite of the remarkably thin pile fabrics degraded lift and drag performance of the airfoil. In case of the control by relatively thin Urethane, even if airfoil surface was largely covered, there had no reduction of aerodynamic noise but little degradation of lift and drag performance. In case of the control by Net, there had least degradation of lift and drag performance among the materials and a little reduction of aerodynamic noise in post-stall condition about 1.8dB.